This issue of The Nation's Report Card highlights mathematics in 2003. It includes sections on Average Scale Scores, Students Reaching NAEP Achievement Levels, Percentile Results, 2003 Assessment Design, State Results, Subgroup Results, Sample Mathematics Questions, Technical Notes, Additional Data Tables, and NAEP on the Web. (AMT)

Topics: ERIC Archive, Achievement, Mathematics, Scores

Every teacher of mathematics, whether at the elementary, middle, or high school level, has an individual goal to provide students with the knowledge and understanding of the mathematics necessary to function in a world very dependent upon the application of mathematics. Instructionally, this goal translates into three components: (1) conceptual understanding; (2) procedural fluency; and (3) problem solving. The mathematics standard presented in this document states that students will: (1)...

Topics: ERIC Archive, Grade 8, Mathematics Education

Each year, students in my seventh- and eighth-grade math classes plan and organize a schoolwide popcorn sale. This activity brings to life mathematical concepts learned in the classroom. By transferring textbook mathematics to a real-world situation, my students learn to value the mathematics being studied and are able to understand how it can affect them in the future. To conduct this lesson, we use several technologies, including the TI-83 Plus to find the best selling price for the popcorn...

Topics: ERIC Archive, Mathematics Instruction, Levert, Brenda

It is always interesting to challenge more capable students with things that they have tended to take for granted. One area in particular that students often tend to overlook in their senior years concerns the important understandings associated with domains and ranges of functions. In this article, the author shares a few favourite questions that he has collected and used many times over the years, and which always result in valuable discussion, frequent bursts of insight, and more than the...

Topics: ERIC Archive, Mathematics, Mathematics Instruction, High Schools, Arnold, Stephen

Prime numbers play an extremely important role in modern mathematics. Apart from still being the object of intense research activity, their applications in banking and security underline a key phenomenon: in the modern world, useful applications of mathematics often come from very "pure" abstract theories. Curiously, despite their undeniable importance, prime numbers are largely absent from school curricula. Prime numbers are typically encountered in Year 7. There one looks at the...

Topics: ERIC Archive, Numbers, Modern Mathematics, Mathematics Instruction, Cairns, Grant

Secondary math students are often heard to ask these two timeless questions: ?When are we ever going to use this?? and ?Why do we need to know this?? We must be able to provide satisfactory answers to these questions, because students who fail to realize the relevance of content covered in class are often less successful than those who do see the immediate value of the knowledge.

Topics: ERIC Archive, Mathematics Instruction, Bryan, Joel A.

GRADES OR AGES: Kindergarten. SUBJECT MATTER: Using Cuisenaire rods. ORGANIZATION AND PHYSICAL APPEARANCE: The guide contains a short introductory section followed by a sequential series of 40 lessons. Diagrams are interspersed throughout the text. The guide is mimeographed and spiral bound with a soft cover. OBJECTIVES AND ACTIVITIES: The introductory section describes the objectives of using Cuisenaire rods. Each lesson contains a detailed sequence of activities with the rods designed to...

Topics: ERIC Archive, Curriculum Guides, Kindergarten, Mathematics Curriculum

This report summarizes evidence from studies that estimate the effects of interventions for improving the mathematics proficiency of middle school students and that meet What Works Clearinghouse (WWC) evidence standards, usually with some reservations.

Topics: ERIC Archive, Mathematics Achievement, Middle School Students, Intervention, Mathematics Curriculum

This booklet briefly traces the history of algebra up through the present day modern algebra. The use of proofs, matrices, properties of groups, and linear equations and computers are discussed. (DT)

Topics: ERIC Archive, Algebra, Curriculum, Instruction, Mathematics, Mathematics Education, Mathematics...

Reported are results of a study of a sample of 259 students at the University of Massachusetts who scored low on a math placement test and later took precalculus math classes. Several possible conclusions are presented to explain the test results. A significantly higher percentage (p

Topics: ERIC Archive, Academic Achievement, College Mathematics, Higher Education, Mathematics Achievement,...

This is the third part of a three-part SMSG algebra text for high school students. Chapter titles include: Truth Sets of Open Sentences; Graphs of Open Sentences in Two Variables; Systems of Equations and Inequalities; Quadratic Polynomials; and Functions. (MK)

Topics: ERIC Archive, Algebra, Inequality (Mathematics), Mathematics Curriculum, Mathematics Instruction,...

The cubic polynomial with real coefficients has a rich and interesting history primarily associated with the endeavours of great mathematicians like del Ferro, Tartaglia, Cardano or Vieta who sought a solution for the roots (Katz, 1998; see Chapter 12.3: The Solution of the Cubic Equation). Suffice it to say that since the times of renaissance mathematics in Italy various techniques have been developed which yield the three roots of a general cubic equation. Students studying a mathematics...

Topics: ERIC Archive, Algebra, Mathematical Formulas, Mathematics, Mathematics Education, Mathematics...

This newsletter lists references to 88 research reports in mathematics education. Of these, 36 were published in United States Office of Education Research Reports over the period 1956-65, 39 in "Research in Education," and 13 in "Pacesetters in Innovation." Titles, pertinent descriptors, and cost of the document in both microfiche and hardcopy are listed. (GR)

Topics: ERIC Archive, Bibliographies, College Mathematics, Elementary School Mathematics, Mathematics...

The activity "First One Home" in the Shell Centre's "Problems with Patterns and Numbers" Blue Box gives rise to a number of interesting patterns for those looking beyond the basic solution given in the book. The game is for two players, each taking turn and turn about to move a single counter on the grid down and/or to the left until one or the other player can put the counter on the FINISH square. Each move can cover as many squares as the mover likes, within the confines...

Topics: ERIC Archive, Educational Games, Mathematics Activities, Mathematics Instruction, Mathematics...

In this article I sketch three key concepts of a cultural-historical theory of mathematics teaching and learning--the theory of objectification. The concepts are: knowledge, knowing and learning. The philosophical underpinning of the theory revolves around the work of Georg W. F. Hegel and its further development in the philosophical works of K. Marx and the dialectic tradition (including Vygotsky and Leont'ev). Knowledge, I argue, is movement. More specifically, knowledge is a historically and...

Topics: ERIC Archive, Mathematics Instruction, Mathematics Education, Arithmetic, Algebra, Children,...

"Odyssey Math," published by CompassLearning[R], is an interactive, software-based K-8 mathematics curriculum. It includes individualized instructional and assessment tools, as well as an administrative function that allows teachers to track student performance and progress and to generate reports. Lessons employ real-world contexts in which students can apply ideas, tools, and manipulatives, and they allow for individualized assessment and instruction. The What Works Clearinghouse...

Topics: ERIC Archive, Mathematics Curriculum, Computer Assisted Instruction, Mathematics Instruction,...

This booklet summarizes the initial conference of the Canadian Association of Mathematics Teachers. The primary purpose of the conference was to exchange information on objectives, present state and proposed development of mathematics curriculum in the provinces of Canada and to comment on the difficulties experienced in introducing new approaches to mathematics teaching. Reports presented during the conferences are included. These reports are concerned with the changes each province has made...

Topics: ERIC Archive, Conference Reports, Curriculum, Elementary School Mathematics, Mathematics Education,...

Most mathematics teachers agree that technology can be used to promote mathematics teaching and learning. Indeed, the Technology Principle of the National Council of Teachers of Mathematics' "Principles and Standards for School Mathematics" states: "Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. Electronic technologies--calculators and computers--are essential tools for teaching,...

Topics: ERIC Archive, Teaching Methods, Mathematics Teachers, Mathematics Education, Mathematics...

Investigating the relationship between fractions and their equivalent decimal representations helps clarify to students that both representations stand for a single (rational) number on the number line. Since students are taught to perform computations with fractions and also to compute with decimals, performing these computations side-by-side with consistent results further reinforces this, and pulls these two representations into focus. In a way the mystery of these representations is...

Topics: ERIC Archive, Mathematics Instruction, Mathematics Education, Mathematics, Arithmetic, Computation,...

These materials are a part of a series of studies sponsored by the Cambridge Conference on School Mathematics which reflects the ideas of CCSM regarding the goals and objectives for school mathematics K-12. Feasibility Studies 9-13 contain a wide range of topics. The following are the titles and brief descriptions of these studies. Number 9--"Streams of Ideas on Checks, Approximations, and Order of Magnitude Calculations." This paper suggests that students should be made aware of...

Topics: ERIC Archive, Curriculum Development, Elementary School Mathematics, Instructional Materials,...

This teachers' guide was written to be used in conjunction with the student text, An Experimental Text in Transformational Geometry. The guide is intended to help teachers who have responsibility for teaching the topics Motions and Transformations in the Plane. Each section commences with a general discussion concerning the major ideas which are to be developed and understood by the students. In addition, situations and statements which could be difficult for students are identified. Finally,...

Topics: ERIC Archive, Elementary School Mathematics, Geometric Concepts, Geometry, Instructional Materials,...

The reorganization of the traditionally separated branches of mathematics into a unified single study is discussed in this report. First, significant events from 1800 to 1950 in the field of creative mathematics that led to the contemporary view of the nature of mathematics are highlighted. This review is followed by a discussion of significant movements in curricula reform sponsored by international organizations, and persons, which contributed to the unified concept. Then the preparation,...

Topics: ERIC Archive, Curriculum, Curriculum Development, Gifted, Mathematics, Mathematics Education,...

This is the student text for part one of a three-part SMSG algebra course for high school students. The principal objective of the text is to help the student develop an understanding and appreciation of some of the algebraic structure as a basis for the techniques of algebra. Chapter topics include congruence; numbers and variables; operations; real numbers; and properties of addition, multiplication, and division. (RH)

Topics: ERIC Archive, Algebra, Bilingual Education, Instructional Materials, Mathematics Curriculum,...

Two issues of the Soloworks newsletter contain information about the Soloworks project, computer equipment, and the educational philosophy that underlies the student-controlled computer based approach to secondary school mathematics instruction. (JY)

Topics: ERIC Archive, Computer Assisted Instruction, Computer Graphics, Laboratories, Mathematics...

This study is concerned with certain aspects of approximation theory which can be introduced into the mathematics curriculum at the secondary school level. The investigation examines existing literature in mathematics which relates to this subject in an effort to determine what is available in the way of mathematical concepts pertinent to this study. As a result of the literature review the material collected has been arranged in a structured mathematical form and existing mathematical theory...

Topics: ERIC Archive, Algebra, Instruction, Mathematical Concepts, Mathematics, Mathematics Education,...

The possibilities for using graphic calculators to enhance the teaching and learning of mathematics are great. However, the boundaries explode when these powerful tools for learning are connected to data logging devices: a whole new approach to mathematics learning becomes possible. Using real world data to introduce the main functions (which are the bread-and-butter of high school mathematics) invites an experimental approach to the subject and encourages students to engage actively in their...

Topics: ERIC Archive, Mathematics Instruction, Mathematics Activities, Class Activities, Mathematics,...

The following topics are discussed in this state handbook: (1) characteristics of a modern math program (structure, vocabulary, correctness); (2) teacher preparation (program descriptions and source material lists for inservice education and the CUPM recommendations for training math teachers); (3) initiating a modern program in mathematics in a particular school system (programs for different types of students, resources for administrators, guidelines for improving programs); (4) mathematics...

Topics: ERIC Archive, Curriculum, Curriculum Guides, Elementary School Mathematics, Instruction, Modern...

This pamphlet from The Madison Project announces the release of films and other materials for a supplementary mathematics program for grades 2 through 8, and for a course in ninth grade algebra. These materials are designed to be used in conjunction with the regular school program in arithmetic and mathematics. Among the films available are (1) A Lesson With Second Graders, (2) Graphing a Parabola, (3) Guessing Functions, and (4) Inservice Courses 1 and 2. (RP)

Topics: ERIC Archive, Curriculum, Elementary School Mathematics, Films, Instructional Materials,...

The text contains a collection of essays to provide a background of factual information concerning the mathematical sciences in undergraduate education. It is intended for the nonmathematical scientist and the scientifically oriented layman. Contents include: (1) recommendations with regard to increasing the available faculty, strengthening the present faculties, improving the quality of undergraduate education, improving facilities and conditions of work, and problems of the underdeveloped...

Topics: ERIC Archive, College Faculty, College Mathematics, Departments, Mathematical Applications,...

These recommendations cover the graduate course work for a doctorate in mathematics. A strong background is assumed of courses such as those outlined in "A General Curriculum in Mathematics for Colleges" and "Preparation for Graduate Study in Mathematics", some of which are reprinted in an appendix. This document then gives detailed outlines for three one-semester courses in analysis, three in topology, two in algebra, and three in applications. There is also a discussion of...

Topics: ERIC Archive, College Mathematics, Curriculum, Graduate Study, Mathematical Applications,...

This paper offers some reflections on the difficulties of teaching mathematical modeling to students taking higher education courses in which modeling plays a significant role. In the author's experience, other aspects of the model development process often cause problems rather than the use of mathematics. Since these other aspects involve students in learning about and understanding complex problem situations the author conjectures that problems arise because insufficient time within...

Topics: ERIC Archive, Mathematical Models, Learning Strategies, Higher Education, Mathematics Education,...

A brief survey of the elementary number systems is provided. The natural numbers, integers, rational numbers, real numbers, and complex numbers are discussed; numerals and the use of numbers in measuring are also covered. (DT)

Topics: ERIC Archive, Mathematics, Mathematics Education, Number Concepts, Number Systems, Numbers,...

Inversions are transformations of geometric figures, under which straight lines may be mapped to circles, and conversely. The use of such mapping allows development of a unified method of solution for many of the problems of elementary geometry, especially those concerning constructions and "pencils" of curves. This book discusses the inversion transformations and their applications. In the first chapter, inversion transformations and their applications to questions in elementary...

Topics: ERIC Archive, Algebra, College Mathematics, Geometric Concepts, Geometry, Higher Education,...

The Louisiana Educational Assessment Program (LEAP) Grade 11 Test is designed to measure proficiency in four subject areas including English, mathematics, social studies, and science. This guide for mathematics is intended to provide a description of the way in which specific skill areas are assessed on the LEAP test and instructional considerations in promoting proficiency of these target skill areas. Skill areas included are: (1) fractions and operations; (2) decimal numbers and operations;...

Topics: ERIC Archive, Grade 11, High Schools, Mathematical Enrichment, Mathematics Instruction, Mathematics...

Very recently, in the "Australian Association of Mathematics Teachers (AAMT)/Australian Industry Group quantitative report" (2014), concerns were raised that school mathematics is lacking real world application. This report highlighted the gaps between school mathematics and the requirements of the workplace. After interviewing industry representatives to find out what mathematical skills were needed in the workplace, estimation was identified as an essential skill. In this article,...

Topics: ERIC Archive, Computation, Mathematics Skills, Mathematics, Mathematics Instruction, Foreign...

The most important objective when starting a class on a previously unknown branch of mathematics is to ensure that the students enjoy and appreciate the significance of this new aspect of mathematics. Inundating them with a flood of technical terms and definitions without any reality experience is a fast way to send the students out of class perplexed and developing an immediate distaste for trigonometry. The author's recommendation for starting any new aspect of mathematics is to immerse the...

Topics: ERIC Archive, Trigonometry, Mathematics Education, Mathematics Instruction, Secondary School...

When students encounter a set of concepts (or terms or principles) that are similar in some way, they often confuse one with another. For instance, they might mistake one word for another word with a similar spelling (e.g., allusion instead of illusion) or choose the wrong strategy for a mathematics problem because it resembles a different kind of problem. By one proposition explored in this review, these kinds of errors occur more frequently when all exposures to one of the concepts are...

Topics: ERIC Archive, Problem Solving, Learning Strategies, Mathematics, Mathematics Instruction,...

These instructional objectives have been selected from materials submitted to the Curriculum Laboratory of the Graduate School of Education at UCLA. Arranged by major course goals, these objectives are offered simply as samples that may be used where they correspond to the skills, abilities, and attitudes instructors want their students to acquire. These objectives may also serve as models for assisting instructors to translate other instructional units into specific measurable terms. For other...

Topics: ERIC Archive, Behavioral Objectives, College Mathematics, Mathematics, Mathematics Instruction, Two...

This history of binary arithmetic begins with details of Thomas Hariot's contribution and includes specific references to Hariot's manuscripts kept at the British Museum. A binary code developed by Sir Francis Bacon is discussed. Briefly mentioned are contributions to binary arithmetic made by Leibniz, Fontenelle, Gauss, Euler, Benzout, Barlow, DeMorgan, Cantor, Muller, Peano, and Bouton. (DT)

Topics: ERIC Archive, Biographies, Mathematical Enrichment, Mathematicians, Mathematics, Mathematics...

This document represents collaborative efforts to define what is valued and necessary in mathematics education for Pacific region children. Underlying assumptions to these standards include constructivism, communication, problem solving, connections, time for learning, and challenge for all students. The majority of the document contains the standards which are grouped into three grade-level sections, K-4, 5-8, and 9-12, and are based largely on the National Council of Teachers of Mathematics'...

Topics: ERIC Archive, Elementary Secondary Education, Learning Activities, Mathematics Curriculum,...

The first part of Course III focuses on matrix algebra, graphs and functions, and combinatorics. Topics studied include: matrices and transformations, the solution of systems of linear equations, matrix multiplication, matrix inversion and a field of 2 x 2 matrices. The section on graphs and functions considers regions of the plane and translations, functions and solution of equations, operations on functions, and bounded functions and asymptotes. The chapter on combinatorics discusses such...

Topics: ERIC Archive, Algebra, Curriculum Development, Instructional Materials, Mathematics, Modern...

Described and announced are the 1971-1972 Bureau of the Census training programs for foreign statisticians. Programs lasting 11 months are offered in these areas: (1) population statistics and demographic analysis, (2) sampling and survey methods, (3) agricultural surveys and censuses, (4) economic surveys and censuses, and (5) data processing. The objectives of the program are a) to train statisticians and technicians in the variety of skills needed to plan and carry out specified statistical...

Topics: ERIC Archive, College Mathematics, Demography, Educational Programs, Instruction, International...

Written to provide some basic information for parents about the New York State Elementary School Mathematics Program, this pamphlet briefly discusses techniques of number operations on the whole numbers, number systems, sets, and geometric concepts. (DT)

Topics: ERIC Archive, Curriculum, Elementary School Mathematics, Geometric Concepts, Instruction,...

Sets of the Annual High School Mathematics Examination for each year from 1966 through 1972 include a copy of each test and its solution key. No mathematics beyond intermediate algebra and trigonometry is needed for solving the test problems. Prior year examinations are published as Volumes 5 and 17 of the New Mathematics Library. (DT)

Topics: ERIC Archive, Achievement Tests, Evaluation, Mathematics, Mathematics Education, Motivation,...

According to this author, the solution to the "phonics versus whole language" debate over the teaching of reading is balance and a focus on the needs of all students. There is similarly a need, in developing numerate young people, to focus on the teaching and learning of mathematics and mathematics skills some of the time, and on application and tasks some of the time (not necessarily at discrete times). Clearly the balance needs to be flexible and dependent on the particular needs of...

Topics: ERIC Archive, Numeracy, Mathematics Instruction, Mathematics Teachers, Foreign Countries, Learning...

The everyday mathematics processes of structural engineers were studied and analyzed in terms of abstraction. A main purpose of the study was to explore the degree to which the notion of a gap between school and everyday mathematics holds when the scope of practices considered "everyday" is extended. J. Lave (1988) promoted a methodology that treats person-in-activity as an integral whole. Laves approach was used as the researcher conducted 70 hours of ethnographic observation of...

Topics: ERIC Archive, Civil Engineering, Engineers, Mathematics Activities, Mathematics Skills, Research...

The curriculum framework for mathematics identifies beliefs about math, general and specific student outcomes, and illustrative examples agreed upon by the six jurisdictions of Western Canada (Manitoba, Saskatchewan, Alberta, British Columbia, Yukon Territory, and the Northwest Territories). The intent is to communicate clearly high expectations for students in mathematics education and facilitate the development of common learning resources. The Alberta Program identifies student outcomes...

Topics: ERIC Archive, Educational Change, Elementary Secondary Education, Foreign Countries, Mathematics...

This booklet contains copies of the two major presentations at the SMSG Conference on Future Responsibilities for School Mathematics: "A History of Attempts to Improve School Mathematics in the United States" (Phillip S. Jones), and "The Future of Mathematics Education in the United States" (Marshall H. Stone). A summary of the discussions following these two addresses is included, along with a listing of the final recommendations for general operational procedures, research...

Topics: ERIC Archive, Conference Reports, Curriculum, Curriculum Development, Elementary School...

This booklet was designed to increase awareness about the metric system. Why the metric system is being used increasingly is described. Pictures illustrate simple comparisons of the most commonly used units of the metric and customary systems. Calculations using both systems are compared through presentation of three problems. Next, everyday units of measurement are listed. Finally, what metric use will mean in the marketplace, in the home, and at work are discussed. (MNS)

Topics: ERIC Archive, Adult Education, Mathematics Curriculum, Mathematics Education, Mathematics...

This document presents the mathematics curriculum framework of the Connecticut State Department of Education. Program goals are presented before the 10 K-12 content standards for mathematics. Each content standard's performance standards are listed separately for grades K-4, 5-8, and 9-12. (ASK)

Topics: ERIC Archive, Academic Standards, Elementary Secondary Education, Mathematics Achievement,...